3d $$ \mathcal{N}=4 $$ super-Yang-Mills on a lattice

Abstract

Abstract In this paper we explore a new approach to studying three-dimensional $$ \mathcal{N}=4 $$ N = 4 super-Yang-Mills on a lattice. Our strategy is to complexify the Donaldson-Witten twist of four-dimensional $$ \mathcal{N}=2 $$ N = 2 super-Yang-Mills to make it amenable to a lattice formulation and we find that lattice gauge invariance forces the model to live in at most three dimensions. We analyze the renormalization of the lattice theory and show that uncomplexified three-dimensional $$ \mathcal{N}=4 $$ N = 4 super-Yang-Mills can be reached in the continuum limit by supplementing the lattice action with appropriate mass terms.